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Most of the sources that I had read about either talks about anelasticity or viscoelasticity, they don't compare both. From what I have read so far ,both anelastic and viscoelastic materials are the same. And they both show significant amount of time dependent strain component. Is there any difference between these two?

Heatgunner
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Anelastic is a material that exhibits a delay in the deformation with respect to the loading.

enter image description here

figure 1: Anelastic material bevahiour (left: wrt to time, right: stress vs. strain) (source Princeton)

Visco-elastic are materials that the load to obtain the deformation also depends on the strain rate. I.e. How fast the deformation is applied. It might depend on other things. There are different models for the viscoelastic material:

enter image description here

figure 1: common Viscoleastic models (source Dickerson)

So a material can be anelastic and viscoelastic at the same time. They describe different properties which happen to be both related to time. Usually aviscoelastic material exhibits hysteresis which is trademark for anelastic.

NMech
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Anelastic materials have an element of time delay between stress and strain, and a time-dependent relaxation of strain. Wikipeidia link

But the viscoelastic materials have both properties of elastic and viscous materials when undergoing deformation.

Viscous materials resist shear flow. And have defusion of atoms under stress as compared to bond stretching along crystallographic planes.

stress strain curve

Stress–strain curves for a purely elastic material (a) and a viscoelastic material (b). The red area is a hysteresis loop and shows the amount of energy lost (as heat) in a loading and unloading cycle. It is equal to , where is stress and is strain.1

Viscoelastic- Wikipedia link.

kamran
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